How to Calculate Pot Odds and Equity in Texas Holdem

The game can be made fair by forcing John and Tom to alternate roles from hand to hand. The articles in the following table are the most common uses of mathematics in poker: River Probability we will hit our Outs — Number of Outs x 2. Basic math rules say that whatever you do to one side of a ratio, you must do to the other. Subscribe to thepokerbank I'll send you an email if I add something new and interesting to the website. Pat Dittmar - " Practical Poker Math " 2.

Basic Texas Holdem Math

How to Calculate Poker Odds

Because two fours are on the flop, let's say the four of hearts and the four of diamonds, so you know that your opponent has to have the four of clubs and the four of spades. The chances of the first card in their hand being one of these two cards are two out of If they get one of them as the first card that leaves the single other card they need out of 51 unseen cards, or one out of Some of the math we discuss on this page can be complicated and the truth is some players won't be able to use it all.

But that doesn't mean they can't be winning Texas holdem players. The math covered in this section forms the building blocks for the advanced math covered lower on the page. Every Texas holdem player can use the basic math included in this section, and if you aren't using it yet you need to start right away. At the most basic level of Texas holdem everything starts with your starting hand.

As we mentioned above, mathematically the player who stars the hand with the better starting hand wins more than the player with the inferior hand.

This means the first math lesson you need to learn and start using is to play better starting hand on average than your opponents. While this can get complicated, especially in games with many multi way pots, you still need to learn how to play better starting hands.

If you take nothing else from this page, if you simply tighten up your starting hand selection it'll immediately improve your results. It's difficult to directly relate position to mathematics, but the main thin to know is the later your position, the better your chances to play in a positive expectation situation.

We'll discuss expectation in a later section, but it's important to understand that having position on an opponent is a strong advantage that equates to a mathematical advantage over the long run.

One of the most important skills Texas holdem players need to develop is the ability to determine the number of outs, or cards remaining in the deck that can complete the hand they're drawing to.

You use this information to determine your chances of winning the hand as well as to determine the pot odds. Pot odds are discussed in the next section, but they show you whether or not a call is profitable in the long run when an opponent makes a bet. We can determine how many outs you have because we know what's in the deck and what we need to improve our hand.

If you have a king, queen, jack, and 10 after the turn you know any of the four aces or four nines complete your straight. This means you have eight outs. You've seen six cards, so the deck has 46 cards remaining in it. Don't make the mistake of thinking about the cards that have been folded or your opponent holds. You haven't seen these cards so any unseen card is still considered a possible river card. In other words, on average, if you play this situation 46 times you're going to complete your straight eight times and not complete it 38 times.

You should always consider how many outs you have in every situation while playing. B knowing your outs you have another piece of information that can help you make profitable decisions throughout the hand. The next question many players ask after they learn how to determine their out sis how they can use this information to make more money at the table. This is where pot odds come into play. Pot odds are simply a ratio or comparison between the money in the pot and the chances you have of completing your hand.

You use this ratio to determine if a call or fold is the best play based on the information you currently have. If you consider the example in the last section concerning the straight draw, you know that the deck holds eight cards that complete your straight and 38 cards that don't. This creates a ratio of 38 to 8, which reduces to 4.

You reduce by dividing 38 by 8. The way you use this ratio is by comparing it to the amount of money in the pot and how much you have to put into the pot. If the pot odds are in your favor it's profitable to call and if not you should fold. If you're in the situation described above of drawing to a straight on the river you can see that a call is correct because the pot is offering 10 to 1 and you have a 4.

Pot odds can get complicated, especially when you start considering how they work when you're determining the correct play with both the turn and river to come. Fortunately charts are available to quickly check the odds of hitting your hand based on how many outs you have. We've included one next so all you have to do is determine your outs and compute the odds the pot is offering. Then compare the two to see if it's profitable to call or fold.

When you're determining your pot odds for the turn and river you determine them on the turn and then if you don't hit your draw you determine them again on the river. This often happens, especially in limit Texas holdem. But if an opponent moves all in on the turn you simply use the turn and river combined odds in your decision. Many beginning Texas holdem players look at a discussion about expectation and instantly decide it's too hard and ignore it. When they do this they severely hurt their long term chances at being a profitable player.

We've broken down how to look at situations while playing poker in a simple manner that almost any player can use below. Do yourself a favor and go into this with an open mind. Once you understand it at a simple level you can learn more as you gain experience.

You may be surprised at just how easy it gets to determine positive and negative expectation with a little practice. Expectation is what the average outcome will be if you play the same situation hundreds or thousands of times. Once you determine the expectation you know if a situation offers positive or negative results on average.

Your goal as a Texas holdem player is to play in as many positive expectation situations as possible and avoid as many negative expectation situations as possible. You need to understand that expectation is something that can be applied to almost any situation in poker, but it's also subjective in many areas.

The problem is determining whether a situation is positive or negative expectation when you sit down at a table with some players who are better than you and some who are worse. You can find many situations where it's easier to determine expectation mathematically, and we'll teach you how to do this now.

While this may seem overly complicated at first, especially to do at the table while playing, you don't need to know exactly how negative or positive a situation is, you only need to know if it's positive or negative. Once you know your pot odds you must use this information appropriately. You do this by connecting the pot odds to the value of your hand.

This means you are able to put your opponents on likely hands and understand your chances of making a better hand than theirs. For example, you have a flush draw on the flop in Hold'em and you are up against an opponent who you think has at least top pair.

There are 9 cards usually referred to as outs that will give you a flush when you have flopped four cards to a flush. This means that you need pot odds of at least to make a call on the flop profitable. Implied odds are defined as the relationship between the size of the current pot and the pot you are expected to win.

This means that occasionally the pot does not lay the correct odds even when you decide to play because you expect to get further action and win more when you hit your hand. But, if you expect your opponent to call a bet or raise on the river if you make your hand, your implied odds are or If you dropped in on this article looking for a Pot Odds Calculator, there are a few simple ones out there online but the truth is you have all the tools you need to calculate pot odds right in your head.

In fact it's much better for your game long term to learn the quick shortcuts and how to calculate pot odds in your head on the fly; it's not like you can pull out and use a pot odds calculator at the poker table anyway.

In order to calculate your equity your odds of winning the pot , you need to first know how many outs you have to make your hand. This becomes quick and simple with a little practice and a little memorization. If you have an open-ended straight draw there are two different values of cards that will give you your hand:. If you have a flush draw there are 13 cards of that suit.

You hold two of them and two of them are on the board:. Remember to remove the outs of cards you know on the board and in your hand and to not count outs twice for example, if you have an open-ended straight flush draw you have 15 outs. When counting your outs you need to remember the idea of anti-outs and possibly even blockers.

If by making your straight you also complete the flush of your opponent, then those straight cards are not outs to your hand and can't be counted as such. The possibility of a flush draw on the board can turn a profitable eight-out straight draw into a six-out straight draw, rendering your odds insufficient.

More about Anti-Outs and Blockers here. If you can't make an astute deduction of the value of your opponent's hands, err on the side of caution and always assume that they have the hand most dangerous to your own. If there's a flush draw, assume they have the draw; if the board is paired, assume they have a full house or, if you're lucky, just trips. It's less expensive to wrongly fold a hand than to wrongly call off your whole stack. There's a simple formula you can remember to get a slightly more accurate figure:.

Without this little formula the percentage would be higher by seven points, giving us an artificially large result. If your equity calculations are wrong you can't make informed decisions. As you can see, equity and pot odds hang on a bunch of relatively simple calculations. All that they require is some memorization of the formulas and techniques and a little bit of practice calculating them in your head. For some people this will be much easier than for others but everyone can do it if they spend a small amount of time practicing.

Remember that implied odds change the game of No-Limit Hold'em greatly. In fact, having a very large amount of implied odds can render a call correct even though pot odds would render it absolutely incorrect.

To learn more about implied odds and how they can affect the choices of you and your opponents check out this Implied Odds article here. For another method of calculating your equity in a pot - one you may find easier - you can check out this Equity article. You can't consider things you don't know, ever.

On average over the long run you will win as if you had 15 outs because you are that much more likely to have every card make you win than none, or some where between. But you'll most likely have to bet twice.

Shoving would avoid this, or being last to act and checking the turn, if possible, then these equity calculations are accurate. But you only get one card for that bet, and your equity is When you are playing Omaha with nine or ten players, with ten after the burn and flop you only have eight cards left. When you have a hand with fifteen outs, how does that work with only eight cards left in the deck??

Thanks to anyone who can reply. Dear Sean, Maybe I'm just stupid, but I want to post this question anyway; To calculate your equity there are multiple ways: As for an example: I figure the 3th one, which would be the one I would use for more accurate odds.

Awaiting your reply, Me. Maybe I'm too new at calculating my outs, but I have read two different ways to do it, and both give different ratios. The first being the one described above. If I had 8 outs on the flop.

How to Calculate Poker Equity